Question:

Given: In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $3/4$ be probability that he knows answer and $1/4$ be probability that he guesses. Assuming that a student who guesses at answer will be correct with probability $1/4$. What is probability that student knows answer given that he answered correctly?
Step 1: Formulate initial mathematical setup / substitution:
Given equation / conditions:
$$P(E1)$$
[1.0 Mark]
Step 2: Perform intermediate algebraic / calculus operations:
Executing the step-by-step reduction:
$$1, P(C|E2)$$
[1.0 Mark]
Step 3: Evaluate final values / boundary conditions:
Substituting limits or solving the simplified system:
$$12/13.$$
[1.0 Mark]
Conclusion: The final evaluated answer is 12/13..

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🎯 Official CBSE Marking Scheme:
Formulating mathematical relation: 1.0 Mark
Executing algebraic/calculus operations: 1.0 Mark
Evaluating final solution/vector: 1.0 Mark